Inquiries to agents from Rightmove are at near-record levels, and 16% up on this time a year ago, the portal said this morning.

It said that over the last month, inquiries have been running at their second highest-ever level.

Asking prices for properties new to the market have bounced up 0.9% following August’s fall, and now stand at an average £264,875.

Miles Shipside, Rightmove director, said: “We usually see a price fall at this time of year as potential home-movers are generally still in holiday mode.

“However, it looks like there are early signs of a bounce-back in demand after the summer lull, leaving those estate agents with a shortage of stock at a potential disadvantage and therefore eager to attract new instructions.

“While there is more property coming to market this year, it has been more than swallowed up by increased sales.

“There is already 10% less property available per branch compared to this time a year ago.”

Asking prices went up over the last month in every region except for the north-west, west midlands and Wales (down 0.8%, 0.7% and 1.1% respectively).

The area with the most price growth was East Anglia at 3.7%.

Across Greater London, new asking prices moved upwards by 0.9%, but this figure disguised dips in areas such as Kensington & Chelsea (down 3.7%) and Westminster (down 2.1%).